The majority (nearly all) of 'stones' come from the gallbladder.
If you have diagnosed Gallstones then it means that your gallbladder isn't working properly and doesn't contract or expand in a regular cycle that allows for complete emptying. This results in the gallbladder bile being of the incorrect balance and globules form almost immediately. The small globules escape and congregate in the intestine. Larger pieces build up in the gallbladder and impede the emptying of the gallbladder. As the gallbladder continues to contract and expand the globules are compacted into a larger pieces. The inability to contract fully causes biliary pain. Some of the larger globs can block the gallbladder neck causing greater biliary pain.
When the gallbladder becomes stagnant the bile coalesces into what it commonly known as sludge where crystals of cholesterol form and can be seen on ultrasound. This sludge can be small like a pea or nearly as large as the gallbladder itself. Below this sludge layer are the Gallstones in the very base of the gallbladder.
The stones you see when you flush consist of the stones from the intestines, the newly formed ones in the gallbladder, some older stones from the gallbladder which are dark green, perhaps some sludge which is often tan coloured.
The large pieces of sludge are difficult to get out but it is possible. These large pieces of sludge look like this:
When the sludge is out you'll get access to the stones.
This picture illustrates a gallbladder with the bile and any small grain sized globules removed it shows the floaters near the neck, a large ball of sludge and some stones in the base.
This scenario is very general and there are many variations as well as other types of stones cause by metabolic changes and infection. Gallbladder problems are in the main caused by high cholesterol, low bile salts and poor contraction. The bile from the live is soluble in water but the gallbladder bile isn't and consequently will form globules in water. Bile from the liver entering the gallbladder in the upper layer will not easily mix so has a tendency to naturally form globules. Because the concentrated bile is in the base of the gallbladder rather than the top it fills and empties in a manner that uses bile from the base unless it is restricted by poor gallbladder functioning.